"A pot of hot water is much better than many exercises" used to say Glenn Gould, who apparently would immerse his arms in hot water for half an hour before sitting at the piano rather than doing various warm-ups or technical exercises; regarding the latter, he specifically said they took away the spontaneity of his approach to the piano and the desire to make music...
There are those who need to warm up. Personally, I don't feel the need, but instead I feel that playing every day is decisive... even if only a little, with a truly spontaneous approach. It is evident that during studies one must examine and resolve the technical formulas proposed by specific texts (I recommend Rossomandi). To know the essence of the difficulties and not repeat them mechanically. This is what I think. For example, it is important to resolve the thumb passage in scales and arpeggios, rather than repeating, repeating even in a wrong way. Learning to perceive muscular tensions and let them go. Developing a great energy that stems from relaxation, balance, and the involvement of both small and large muscles.........
I believe that it is a very individual and physiological matter. I have tried several times to warm my hands with hot water bottles or immerse them in hot water. It is certainly much better than playing them cold, but personally, the only thing that truly allows me to think and play what I am thinking is warming up well at the piano. A proper warm-up for my physiology can even last about an hour.